Pocket Cube

Solved Pocket Cube

File:Pocket cube.jpg

Scrambled Pocket Cube

File:Pocket cube tilt.jpg

Pocket Cube with one side tilted

The Pocket Cube (also Mini Cube or Ice Cube [1]) is the 2×2×2 equivalent of a Rubik's cube. The cube consists of 8 corner pieces, and no other types of cubies.

Permutations

Any permutation of the 8 corner cubies is possible (8 positions), and 7 of the cubies can be independently rotated (3⁷ positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. The number of possible positions of the cube is

${\frac {8!\,3^{7}}{24}}=7!\,3^{6}=3674160$

The maximum number of turns required to solve the cube is up to 11 full turns, or up to 14 quarter turns. An optimal (least number of turns) solution from any position can be found by a computer with a brute force algorithm.

The number f of positions that require n full twists and number q of positions that require n quarter turn twists are:

n	f	q
0	1	1
1	9	6
2	54	27
3	321	120
4	1847	534
5	9992	2256
6	50136	8969
7	227536	33058
8	870072	114149
9	1887748	360508
10	623800	930588
11	2644	1350852
12		782536
13		90280
14		276

Records

Mátyás Kuti, from Hungary holds the world record for the fastest time solving the pocket cube in competition, with a time of 2.73 seconds set at the Czech Open in 2007.

Trivia

At Rubik's online store, an easier version of the Pocket Cube exists, dubbed the "Junior Cube." [2]. This version has only two colors, with a picture of a monkey on one face.

See also

• Pyramorphix, a pyramidal puzzle that uses the same mechanism
• Rubik's Cube (3×3×3)
• Rubik's Revenge (4×4×4)
• Professor's Cube (5×5×5)
• Speedcubing